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12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
12X1 T08 01 binomial expansions
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12X1 T08 01 binomial expansions

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Transcript

  • 1. Binomial Theorem
  • 2. Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
  • 3. Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
  • 4. Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
  • 5. Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
  • 6. Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
  • 7. Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
  • 8. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle
  • 9. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1
  • 10. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1
  • 11. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1
  • 12. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1
  • 13. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1
  • 14. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1
  • 15. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1
  • 16. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1
  • 17. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1
  • 18. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1
  • 19. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1
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  • 33. Exercise 5A; 2ace etc, 4, 6, 7, 9ad, 12b, 13ac, 14ace, 16a, 22, 23

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